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Article Dans Une Revue Israel Journal of Mathematics Année : 2017

The boundary of the outer space of a free product

Résumé

Let $G$ be a countable group that splits as a free product of groups of the form $G=G_1\ast\dots\ast G_k\ast F_N$, where $F_N$ is a finitely generated free group. We identify the closure of the outer space $P\mathcal{O}(G,\{G_1,\dots,G_k\})$ for the axes topology with the space of projective minimal, \emph{very small} $(G,\{G_1,\dots,G_k\})$-trees, i.e. trees whose arc stabilizers are either trivial, or cyclic, closed under taking roots, and not conjugate into any of the $G_i$'s, and whose tripod stabilizers are trivial. Its topological dimension is equal to $3N+2k-4$, and the boundary has dimension $3N+2k-5$. We also prove that any very small $(G,\{G_1,\dots,G_k\})$-tree has at most $2N+2k-2$ orbits of branch points.

Dates et versions

hal-01059082 , version 1 (29-08-2014)

Identifiants

Citer

Camille Horbez. The boundary of the outer space of a free product. Israel Journal of Mathematics, 2017, 221 (1), pp.179-234. ⟨10.1007/s11856-017-1565-0⟩. ⟨hal-01059082⟩
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